Twisted Poincare duality for some quadratic Poisson algebras

Launois, Stephane and Richard, Lionel (2007) Twisted Poincare duality for some quadratic Poisson algebras. Letters in Mathematical Physics, 79 (2). pp. 161-174. ISSN 0377-9017. (Full text available)

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http://dx.doi.org/10.1007/s11005-006-0133-z

Abstract

We exhibit a Poisson module restoring a twisted Poincaré duality between Poisson homology and cohomology for the polynomial algebra R=C[X1Xn] endowed with Poisson bracket arising from a uniparametrised quantum affine space. This Poisson module is obtained as the semiclassical limit of the dualising bimodule for Hochschild homology of the corresponding quantum affine space. As a corollary we compute the Poisson cohomology of R, and so retrieve a result obtained by direct methods (so completely different from ours) by Monnier.

Item Type: Article
Uncontrolled keywords: Poisson (co)homology - Hochschild (co)homology - Poincaré duality
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Pure Mathematics
Depositing User: Stephane Launois
Date Deposited: 03 Jun 2008 14:28
Last Modified: 28 May 2014 10:56
Resource URI: http://kar.kent.ac.uk/id/eprint/3154 (The current URI for this page, for reference purposes)
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